Definition 4.9.7.  Let u ∈ ℕ. We define:
Monu := [Mon(Hom(A, B))A,B ∈ Mon(idC)C ∈ Mon(∘)D,E,F ∈ Mon]u is a/an u-small category
Remarks.

The objects of this category are actually isomorphism classes of monoids.

References.